NOVEL FORMULATIONS AND PROTOTYPICAL SOLUTION TEMPLATE FOR TIME-BASED RECURSIONS OF EQUIPMENT REPLACEMENT PROBLEMS WITH STATIONARY PERTINENT DATA

This research article used the state concept to obtain the structure of the sets of feasible replacement times corresponding to various decision times, in equipment replacement problems, thereby obviating the need for network diagrams for such determination. It went further to undertake novel formulations of the equipment replacement problems, incorporating cardinality analyses on the feasible transition states for each feasible time. The proofs were achieved by deft deployment of change of variables technique, maximum equipment operational age constraint and appropriate set addition definition. In the sequel, the article designed solution implementation templates for the corresponding dynamic programming recursions. These templates circumvent the inherent tedious and prohibitive manual computations associated with dynamic programming formulations and may be optimally appropriated for sensitivity analyses on such models in just a matter of minutes.